Polytope of Type {2,2,6,3,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,6,3,6}*864
if this polytope has a name.
Group : SmallGroup(864,4704)
Rank : 6
Schlafli Type : {2,2,6,3,6}
Number of vertices, edges, etc : 2, 2, 6, 9, 9, 6
Order of s₀s₁s₂s₃s₄s₅ : 6
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,6,3,6,2} of size 1728
Vertex Figure Of :
   {2,2,2,6,3,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,2,2,3,6}*288, {2,2,6,3,2}*288
   9-fold quotients : {2,2,2,3,2}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,6,3,6}*1728, {2,4,6,3,6}*1728, {2,2,6,6,6}*1728f
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := (14,23)(15,24)(16,25)(17,26)(18,27)(19,28)(20,29)(21,30)(22,31);;
s3 := ( 5,14)( 6,16)( 7,15)( 8,20)( 9,22)(10,21)(11,17)(12,19)(13,18)(24,25)
(26,29)(27,31)(28,30);;
s4 := ( 5, 9)( 6, 8)( 7,10)(11,12)(14,27)(15,26)(16,28)(17,24)(18,23)(19,25)
(20,30)(21,29)(22,31);;
s5 := ( 8,11)( 9,12)(10,13)(17,20)(18,21)(19,22)(26,29)(27,30)(28,31);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s3*s4*s3*s4*s3*s4, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, 
s5*s3*s4*s5*s4*s5*s3*s4*s5*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(31)!(1,2);
s1 := Sym(31)!(3,4);
s2 := Sym(31)!(14,23)(15,24)(16,25)(17,26)(18,27)(19,28)(20,29)(21,30)(22,31);
s3 := Sym(31)!( 5,14)( 6,16)( 7,15)( 8,20)( 9,22)(10,21)(11,17)(12,19)(13,18)
(24,25)(26,29)(27,31)(28,30);
s4 := Sym(31)!( 5, 9)( 6, 8)( 7,10)(11,12)(14,27)(15,26)(16,28)(17,24)(18,23)
(19,25)(20,30)(21,29)(22,31);
s5 := Sym(31)!( 8,11)( 9,12)(10,13)(17,20)(18,21)(19,22)(26,29)(27,30)(28,31);
poly := sub<Sym(31)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s3*s4*s3*s4*s3*s4, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, 
s5*s3*s4*s5*s4*s5*s3*s4*s5*s4 >;

to this polytope